Finite Group Databasebeta

← #21446461

Subgroups — #21446461

Order 7808.

254 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519711C211yesmaximal, characteristic
2C2×#14519702C211yesmaximal, characteristic
3C2×#14519702C211yesmaximal, characteristic
4#16839668C211yesmaximal, characteristic
5C4×C4⋊Dic61C211yesmaximal, characteristic
6#16839525C211yesmaximal, characteristic
7C61×#336C211yesmaximal, characteristic
8C22×Dic122C2211yescharacteristic
9C2×C4⋊Dic61C2211yescharacteristic
10C2×C4⋊Dic61C2211yescharacteristic
11C2×C4⋊Dic61C2211yescharacteristic
12C2×C4×Dic61—21no—
13#14519711—22no—
14#14519702—22no—
15#14519702C414yescomplemented
16#14519684—21no—
17#14519684—21no—
18#14519684—21no—
19C22×C8×C61C2211yescharacteristic
20C22×C8×C61C2211yescharacteristic
21C2×C42×C61C2211yescharacteristic
22C22×C4×C61D411yescharacteristic
23C22×C4×C61D411yescharacteristic
24C22×C4×C61C2311yescharacteristic
25C22×Dic61—21no—
26C22×Dic61—21no—
27C22×Dic61—21no—
28C22×Dic61—21no—
29C2×Dic122—21no—
30C2×Dic122—21no—
31C2×Dic122—21no—
32C2×Dic122—21no—
33C2×Dic122—21no—
34C2×Dic122C2×C412yes—
35C2×C8×C61—21no—
36C2×C8×C61—21no—
37C2×C8×C61—21no—
38C2×C8×C61—21no—
39C2×C8×C61—21no—
40C2×C8×C61C2×C412yes—
41C42×C61—21no—
42C42×C61—21no—
43C4⋊Dic61—21no—
44C4⋊Dic61—21no—
45C4⋊Dic61—21no—
46C4⋊Dic61—21no—
47C4⋊Dic61C2×C412yes—
48C4⋊Dic61D412yes—
49C4×Dic61—42no—
50C23×C61C2×D411yescharacteristic
51C2×C4×C61—21no—
52C2×C4×C61—21no—
53C2×C4×C61—21no—
54C2×C4×C61—21no—
55C2×C4×C61—21no—
56C2×C4×C61Q1612yes—
57C2×C4×C61C22×C411yescharacteristic
58C2×C4×C61C2×D411yescharacteristic
59C2×C4×C61#4111yescharacteristic
60C2×C4×C61#4111yescharacteristic
61C2×C4×C61#4111yescharacteristic
62C2×C4×C61#4111yescharacteristic
63C2×Dic61—22no—
64C2×Dic61—22no—
65C2×Dic61—22no—
66C2×Dic61—41no—
67C2×Dic61—41no—
68C2×Dic61—41no—
69C2×Dic61—41no—
70C2×Dic61—41no—
71C2×Dic61—41no—
72C2×Dic61—41no—
73C2×Dic61—41no—
74C2×Dic61—41no—
75Dic122—22no—
76Dic122—22no—
77Dic122—41no—
78Dic122—41no—
79C8×C61—22no—
80C8×C61—41no—
81C22×C61C4×D411yescharacteristic
82C22×C61#12111yescharacteristic
83C22×C61#12311yescharacteristic
84C22×C61C2×Q1611yescharacteristic
85C22×C61#13511yescharacteristic
86C22×C61AGL(1,ℤ/8)11yescharacteristic
87C22×C61#13711yescharacteristic
88C4×C61—22no—
89C4×C61—41no—
90C4×C61#11711yescharacteristic
91C4×C61C4×D411yescharacteristic
92C4×C61#12411yescharacteristic
93C4×C61#12611yescharacteristic
94Dic61—42no—
95Dic61—42no—
96Dic61—42no—
97Dic61—81no—
98#1928—611nomaximal, Sylow
99C2×C61#38811yescharacteristic
100C2×C61C4×Q1611yescharacteristic
101C2×C61#44011yescharacteristic
102C2×C61#46211yescharacteristic
103C2×C61#46311yescharacteristic
104C2×C61#48411yescharacteristic
105C2×C61#48511yescharacteristic
106C2×#107—611no—
107C2×#103—611no—
108C2×#103—611no—
109#391—611no—
110C4×C4⋊C4—611no—
111#340—611no—
112#336D6111yescharacteristic
113C61#192811yescharacteristic, complemented, Sylow
114C22×Q8—611no—
115C22×C8C2×D6111yescharacteristic
116C22×C8C2×D6111yescharacteristic
117C2×C4⋊C4—611no—
118C2×C4⋊C4—611no—
119C2×C4⋊C4—611no—
120C2×C42—1221no—
121C2×C42C2×D6111yescharacteristic
122#107—1222no—
123#103—614no—
124#103—1222no—
125#95—1221no—
126#95—1221no—
127#95—1221no—
128C2×Q8—612no—
129C2×Q8—1221no—
130C2×Q8—1221no—
131C2×Q8—1221no—
132C2×Q8—1221no—
133C2×Q8—1221no—
134C22×C4—1221no—
135C22×C4—1221no—
136C22×C4—1221no—
137C22×C4—1221no—
138C22×C4D24411yescharacteristic
139C22×C4D24411yescharacteristic
140C22×C4C22×D6111yescharacteristic
141C2×C8—21no—
142C2×C8—21no—
143C2×C8—21no—
144C2×C8—21no—
145C2×C8—21no—
146C2×C8C4×D6112yes—
147C4⋊C4—612no—
148C4⋊C4—612no—
149C4⋊C4—1221no—
150C4⋊C4—1221no—
151C4⋊C4—1221no—
152C4⋊C4—1221no—
153C42—21no—
154C42—21no—
155C42—2442no—
156C23C2×D24411yescharacteristic
157Q8—1222no—
158Q8—1222no—
159Q8—2441no—
160Q8—2441no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—1222no—
167C2×C4—1222no—
168C2×C4—1222no—
169C2×C4—2441no—
170C2×C4—2441no—
171C2×C4—2441no—
172C2×C4—2441no—
173C2×C4—2441no—
174C2×C4—2441no—
175C2×C4—2441no—
176C2×C4—2441no—
177C2×C4—2441no—
178C2×C4Dic24412yes—
179C2×C4C2×C4×D6111yescharacteristic
180C2×C4#1175822211yescharacteristic
181C2×C4D4×D6111yescharacteristic
182C2×C4#1175822411yescharacteristic
183C2×C4#1175822411yescharacteristic
184C2×C4#1175822611yescharacteristic
185C8—22no—
186C8—41no—
187C22C4×D24411yescharacteristic
188C22#1451975211yescharacteristic
189C22#1451976111yescharacteristic
190C22C2×Dic24411yescharacteristic
191C22#1451979911yescharacteristic
192C22#1451980511yescharacteristic
193C22#1451981011yescharacteristic
194C4—22no—
195C4—41no—
196C4—4881no—
197C4—2442no—
198C4—2442no—
199C4—2442no—
200C4#1451973511yescharacteristic
201C4#1451973711yescharacteristic
202C4#1451976311yescharacteristic
203C4#1451977211yescharacteristic
204C2#1683965411yescharacteristic
205C2C4×Dic24411yescharacteristic
206C2#1683986411yescharacteristic
207C2#1683997311yescharacteristic
208C2#1683997811yescharacteristic
209C2#1684009811yescharacteristic
210C2#1684010411yescharacteristic
subgroupG/H
centerC23C2×D244
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#336C2
socleC23×C61C2×D4
hypercenter#336D61
hypocenterC61#1928
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #336

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
15. #14519702C4semidirect
113. C61#1928semidirect